02 April 2012

(parenting) Bite-sized math/sci lessons for 5 yr olds: # 1-11

Hi,

For the last few weeks, every other night, our 5 yr-old and I do a couple of bite-sized "lessons" about ideas in math or science. They take us about 3 minutes each, and are fun. He's come to ask, "is tonight lesson night?" Since he's getting a kick out of it, I'll post our first 11 lessons in case your'e looking for ideas of doing the same.

I hope our five year old won't mind that I'm putting this online, forever in Google's memory banks...

Preliminary: We reserve a special 6" x 9" spiral-bound notebook for these, and we dutifully label the top of each page with the lesson number and name. (Honest, this is part of the fun.) We assume you already are doing stuff like multiplication of single-digit numbers, and have watched some sciencey stuff like They Might Be Giants's DVDs about atoms and DNA and things.

Lesson 1: length, area, volume

Draw three short lines: 1 inch, 2 inches, 3 inches, ticking off the inches. Draw another line. How long is it?

Draw rectangles composed of many 1 x 1 squares. How many squares is each rectangle? What if you multiply the length of one side by the length of the other side?

Write "one-dimensional" by length, and "two-dimensional" by area. Write "three-dimensional." Can you guess what that is? Draw a cube of cubes, etc.

Lesson 2: adding bigger numbers

Add two two-digit numbers, in which carrying is never needed. (E.g., 23 + 34, added vertically.) Your child does some in their own handwriting.

Two lines that make a "T" shape are perpendicular. I like the near-miss form of learning: draw a couple of examples of perpendicular lines, and then provide counterexamples, saying "these are NOT perpendicular lines."

Draw a line, and put a dot along it, and ask your child, "draw the perpendicular line that starts here."

Try to teach the notion of angle. If the lines are perpendicular, the angles are the same on either side of the perpendicular line. The lines are not perpendicular, one angle will be larger than the other.

Lesson 5b: how to know where a laser beam would go if it hits a plane (flat) mirror

My son likes lasers, and kids hear about them in movies like Toy Story, so...

Draw a line segment, with hashmarks on one side to indicate it's the cross-section of a mirror. like this, but without the Thetas. ("normal" is just the physics word for "perpendicular, but in any number of dimensions")

Now explain that people who really like math have a secret key that lets them describe these patterns with just a few little special marks on their paper. First, let's give these numbers special names. Let's call the number we're interested in x[n] ("x sub n"). That's the number we're trying to figure out. Let's call the guy before it x[n-1] ("x sub n minus 1"). That's the guy right before it. And what might we call the number before THAT? (... x[n-2] )

Draw a Sierpinski triangle, or whatever the right name of it is. Draw a triangle. Put a dot at the halfway point of each side. Connect the sides to draw a new triangle inside. Put a dot at all 9 new halfway points. Draw 3 triangles. And so on. FOR-EV-ER!

Lesson 9: "Daddy's Square"

I don't know the name for this. Basically you draw an inward-spiraling square, in which the corners are a little less than 90 degrees. Like the last two figures here.

Heat is a kind of energy. When stuff heats up, the atoms and molecules inside jiggle around more and more. So the ice melts, becomes water, becomes steam, eventually the electrons tear off, etc etc. I like presenting it this way, around 4:30 [YouTube, Feynman].

Lesson 10b: Important Temperatures

In America we have a weird way of telling the number of how hot or cold something is. It's called degrees Fahrenheit. Most of the rest of the world calls it something different. Like, here we use inches or miles, and over there they use centimeters and kilometers.

Draw a number line with two ticks on it. The first third is called "ice," the second is "water," and the rightmost third is called "steam." Tick one is 32 (deg) F, and then 212 (deg) F.

Talk about this. Have them recite, "ice becomes water at 32 degrees Fahrenheit." I know it might feel rote to rehearse it this way, but really, I think that is the most sensible thing.

Still awake? Then say, remember how the rest of the world has an easier way of thinking about it? They call their way degrees Celsius, and the numbers are 0 and 100.

There's actually a number way... over... there... (to the left) where if we ever got all the way over, those jiggling atoms would stop. But you can't ever get that far. You can get really close, very very close, but never all the way (etc). This is absolute zero.

Lesson 11: gears

Draw two enmeshed gears

If this one goes this way, which way does the other one spin?

Say this has 10 teeth and the other has 20 teeth. If you spin the big one once, how many times does the little one spin?

What if it's 10 and 30?

What if it's 5 and 10?

Why is this useful? Well, you know how your bike has gears here and here...?

I'd love to hear your informal bedtime lessons if you got 'em. Share! (And if you want a next installment of this, encourage me in the comments.)

G-Fav

ps BONUS: Cosmos is available on Netflix Instant. I've been really shocked at how much of Sagan's teachings stick with our kids. There's evidently a lot of "see that snow? it's from the STARS!" talk, lately.

Also, I have a lasting image in my head of Carl Sagan, on Cosmos, unrolling a really long strip of adding-machine paper (or whatever it was) with a googol written out on it -- a 1 with 100 zeroes. He unrolled it out the door and down the street, I seem to recall. Cosmos definitely does stick!